The law 990/1969 requires that each motor vehicle or trailer standing or moving on a public road have third party insurance (called RCA, Responsabilità civile per gli autoveicoli). Historically, a part of the certificate of insurance must be displayed on the windscreen of the vehicle. This latter requirement was revoked in 2015, when a national database of insured vehicles was built by the Insurance Company Association (ANIA, Associazione Nazionale Imprese Assicuratrici) and the National Transportation Authority (Motorizzazione Civile) to verify (by private citizens and public authorities) if a vehicle is insured. There is no exemption policy to this law disposition.
You’ll notice that none of that liability coverage pays for your car or injuries, nor for any injuries your passengers sustain if you cause a wreck. This is why many people — particularly those whose car isn’t yet paid off — want “full coverage” car insurance. This isn’t actually a type of coverage, but instead typically refers to policies that include liability coverage, plus comprehensive and collision coverages.
Auto insurance is financial protection, and not just for the investment you made when you bought your car. After a really serious accident, bills for damage and injuries can easily reach into hundreds of thousands of dollars. If you happen to cause such a wreck, the victims could sue you. In the worst case scenario, assets such as your savings and home could be seized.